Independent solution

How to solve this Interest Rate Valuation question

Setup

Setup

Use each spot rate only for the payment at its matching maturity.

P=11.0425+11.0452+11.04753+11.054P=\frac{1}{1.0425}+\frac{1}{1.045^2}+\frac{1}{1.0475^3}+\frac{1}{1.05^4}

Model

Model

The sum of the four unit-payment present values is the observed annuity price.

P=3.5677P=3.5677

Compute

Compute

Solve for the single annual effective rate whose four-year annuity factor has that value.

a4‾∣ i=3.5677⟹i=0.0474a_{\overline{4}|\,i}=3.5677\Longrightarrow i=0.0474

Answer

Answer

The equivalent level rate is approximately 4.74%, corresponding to choice C.

i≈4.74%(C)\boxed{i\approx4.74\%\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

Check END/BGN, period, sign, TVM, and cash-flow setup

  1. 2nd CLR TVM; 4 N; 3.5677 +/- PV; 1 PMT; 0 FV; CPT I/YI/Y ≈ 4.74First compute the annuity price from the four spot rates.